Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4290
 Title: The Concept of Separable Connectedness: Applications to General Utility Theory Authors: Induráin, Esteban Keywords: Topological connectedness; separability; ordered topological spaces; utility functions Issue Date: 2001 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: Esteban Induráin, "The Concept of Separable Connectedness: Applications to General Utility Theory", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.2, pp. 89–99. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics32 (2001) suppl.2 Abstract: We say that a topological set X is separably connected if for anytwo points $x,\; y\;\epsilon\; X$ there exists a connected and separablesubset $C\left(x,y\right)\subseteq X$ to which both x and y belong.This concept generalizes path-connectedness. With this concept wehave improved some results on general utility theory: For instance,in 1987 Monteiro gave conditions (dealing with real-valued, continuous,order-preserving functions) on path-connected spaces in order to getcontinuous utility representations of continuous total preorders defi{}nedon the set. We have recently proved (in an article by Candeal, Hervèsand Indurain, published in the Journal of Mathematical Economics,1998) that Monteiro\textquoteright{}s results also work for the moregeneral case of separably connected spaces. Then we study the particularsituation of separable connectedness on spaces endowed with some extrastructure, e.g. metric spaces. Type: Article URI: http://hdl.handle.net/10077/4290 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s2

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